Optimal mean–variance asset-liability management with stochastic interest rates and inflation risks

Abstract

This paper considers an optimal asset-liability management problem with stochastic interest rates and inflation risks under the mean–variance framework. It is assumed that there are $$n+1$$ assets available in the financial market, including a risk-free asset, a default-free zero-coupon bond, an inflation-indexed bond and $$n-2$$ risky assets (stocks). Moreover, the liability of the investor is assumed to follow a geometric Brownian motion process. By using the stochastic dynamic programming principle and Hamilton–Jacobi–Bellman equation approach, we derive the efficient investment strategy and efficient frontier explicitly. Finally, we provide numerical examples to illustrate the effects of model parameters on the efficient investment strategy and efficient frontier.